Construction of a 'human friendly' Rubik's Cube solution with sub-40 average move-count

Construction of a 'human friendly' Rubik's Cube solution with sub-40 average move-count

Since 2010 it is known that a computer implementation of Kociemba's algorithm can solve any scrambling of a Rubik's Cube in at most 20 moves, with a slightly better bound for its average move-count. However, the required look-up tables and searches are extensive; without computers, one cannot hope to do so well on average, given practical memory and time constraints. In this talk we focus on “linear solving,” a hands-on style that mixes aspects of speed-solving, which typically uses around 60 moves without backtracking, and fewest-moves solving, wherein time is allowed for search. We start by reviewing some expert linear solving methods with emphasis on their memory and move-count performance. Then we introduce a hybrid approach with relatively small look-up tables which permits a computational proof, carried out jointly with Joseph Miller, that it averages below 40 moves in the half-turn metric.